WordNet records no synonym and no antonym for bylaw. It is the only member of its synset, which is common for technical, taxonomic and single-sense vocabulary — there is no other English word that means the same thing. The broader and narrower terms below are the useful relations in that case.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
a rule adopted by an organization in order to regulate its own affairs and the behavior of its members
Synonyms, antonyms and the broader and narrower relations for bylaw come from Princeton University’s WordNet. Full sources and licences.